Anisotropic Diffusion in Toroidal geometries

Ahmed Ratnani (1) , B Nkonga (2) , Emmanuel Franck (3) , Alina Eksaeva (4) , Maria Kazakova (5)

1 IPP - Max-Planck-Institut für Plasmaphysik [Garching]
2 MAB - Laboratoire de Mathématiques Appliquées de Bordeaux
3 TONUS - TOkamaks and NUmerical Simulations
4 The National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) [Moscow, Russia]
5 LIH - Lavrentyev Institute of Hydrodynamics

In this work, we present a new Finite Element framework for toroidal geometries based on a tensor product description of the 3D basis functions. In the poloidal plan, different discretizations, including B-Splines and cubic Hermite-Bézier patchs are defined, while for the toroidal direction both Fourier discretization and cubic Hermite-Bézier elements can be used. In this work, we study the MHD equilibrium by solving the Grad-Shafranov equation, which is the basis and the starting point of any MHD simulation. Then we study the Anistropic Diffusion problem in both steady and unsteady states.

Mots clés: anistropic diffusion; iso-parametric; toroidal; splines; grad safranov

Domaines: Analyse numérique [math.NA]

Ahmed Ratnani, B Nkonga, Emmanuel Franck, Alina Eksaeva, Maria Kazakova. Anisotropic Diffusion in Toroidal geometries. ESAIM: Proceedings and Surveys, 2016, ⟨10.1051/proc/201653006⟩. ⟨hal-01120692⟩